Light traveling in a homogeneous medium travels in straight lines. However, When light travels through a medium containing particles of material, the particles scatter the light. For a single particle, the amount of scattering in a particular direction depends upon the size, shape, and composition of the particle and the wavelength of the light. For a collection of particles, light scattered from all of the particles contributes to the total intensity of light scattered in a particular direction relative to the incident light. By measuring the amount or intensity of light scattered throughout a number of angles relative to the incident light, it is possible to infer properties of the particles that induce the scattering. In particular, for particles of small size and similar composition, the pattern of scattered light is indicative of the sizes of the scattering particles. Prior analytical instruments have used the technique of analyzing the scattered light intensity to determine the spectrum of particle sizes for a mixture of small particles of varying sizes. A particle size analyzer using this technique typically samples the angular distribution of the intensity of the light scattered from the mixture, processes the data, and produces numerical values and possibly a graph or a histogram as output. The analyzer output represents the number or volume fraction of scattering particles in the mixture as a function of the size of the particles and is usually called a particle size distribution.
The prior art has provided many different techniques of measuring and analyzing the light scattered by small particles. For example, a technique called optical particle counting has been developed for separately detecting the light scattered by individual particles in extremely dilute concentrations of particles, but this technique is time consuming and is impractical for samples containing a large number of particles. On the other hand, if the concentration of particles is too great, light scatters multiple times from the scattering particles before being observed, and the multiple scatterings obscure the effect of each particle's contribution to the observed intensity of scattered light. Particle size analyzers have therefore primarily addressed the experimental conditions where the concentration of scattering particles is such that each observed light ray is deflected only once by a single scattering particle. Under these conditions, called single scattering, the scattered light has been analyzed either by measuring the time variation of the light scattered in a particular direction or by time averaging the scattered light over a range of directions. The former technique is called dynamic light scattering, and the latter is termed static, or classical, light scattering.
For classical scattering, the problem of relating the angular distribution of scattered light to the size of the scattering particle has been solved mathematically for the case of a spherical particle illuminated by a beam of unpolarized light. The mathematical solution is given by a theory proposed by Gustav Mie. The Mie theory is set forth in Chapter 4 of the book, Absorption and Scattering of Light by Small Particles, by Craig F. Bohren and Donald R. Huffman (John Wiley & Sons, 1983), which book is incorporated by reference. A particle size analyzer may employ the Mie theory to determine particle size distributions from the observed pattern of scattered light. Such an analyzer is not limited to the analysis of only samples containing particles of spherical shape; the sizes are reported as radii of spheres that are equivalent to the actual particles in terms of light scattering. For most applications, the equivalent-sphere specification of a particle size distribution is sufficient to characterize the actual particle size distribution. Mathematical models have also been derived for particular particle shapes other than spherical, but they have been found to have limited value since, for scattering, only the average behavior of a large number of particles is of interest.
Since scattering is also a function of the wavelength of the incident light, prior art analyzers have found it convenient to use incident light of a single wavelength. For this purpose, a laser has been the typical source. Lasers have been used which produce light in the visible and near-visible wavelength range. The descriptions herein of the prior art, and of the invention, use the term "light," but it must be recognized that the scattering being described is a phenomenon of electromagnetic radiation in general. Thus, the term "light" herein should be read as referring to any such radiation that meets whatever constraints are imposed by the characteristics of the various components of the analyzer (such as the transparency of the sample holders at the wavelength of interest and the frequency response of the detectors) the nature of the scattering particles (such as the refractive index and absorption coefficient as a function of wavelength), and the overall construction of the analyzer.
In a typical prior art arrangement, a particle size analyzer has a source of unpolarized light that is projected in a beam to impinge upon a sample. The sample contains the particles whose sizes are under investigation. The particles are dispersed in the region of the sample that is illuminated by the incident light beam. The particles scatter light in patterns that are dependent on the ratio of the size of the particle to the wavelength of the light and on the refractive index of the particle material. The refractive index, a complex function of wavelength, is a measure of how much the light is refracted, reflected, and absorbed by the material. For a beam of unpolarized light incident on a random mixture of small particles, the scattering pattern is symmetric about the axis of the incident beam. The scattering is the result of the refraction, reflection, and absorption by the particles, as well as diffraction at each particle surface where a light ray in the incident beam is tangent to the particle surface.
Light that scatters at a particular angle with respect to the incident beam may be rotated about the beam axis without changing the scattering angle. A large number of rays scattering from a single particle at a given scattering angle will fill all rotational orientations and thus form a cone of light, with the apex at the scattering particle and with the generating angle (one-half the apex angle) of the cone equal to the scattering angle. The pattern of light rays scattering at all angles from a single particle may thus be thought of as made up of a continuous series of open cones of light, with the generating angle for a given cone corresponding to the scattering angle for the light comprising the surface of that cone. The axes of all of the cones are collinear with the line defined by the incident beam and the apexes of the cones are located at the scattering particle. At a distance from the scattering particle, a plane perpendicular to the incident beam will intersect a given cone in a circle. Planes not perpendicular to the incident beam will intersect a given cone in a curved line comprising a conic section, i.e., an ellipse, a parabola, or a hyperbola, depending upon the orientation of the plane. Regardless of form, the curved line of intersection represents a single scattering angle.
In any practical particle size detector, it is not possible or necessary to measure the scattering angle with infinite precision. Nevertheless, better angular resolution in the analyzer provides better particle size resolution. In order to address angular precision effects directly, we will refer to the set of all scattering angles falling between a precise lower angular limit and a precise upper angular limit as an "angle class" of some intermediate angle q. Light scattered within an angle class scatters into the region between two cones of slightly different size. The smaller (inner) of the two cones is generated by the lower angular limit of the angle class and the larger (outer) cone is generated by the upper angular limit. The apexes of both cones are located at the scattering particle.
The inner and outer cones of an angle class define a circular annular region on a plane perpendicular to the incident beam and a more complex shaped region (corresponding to a conic section) on a plane not perpendicular to the incident beam. Scattered light rays intersecting the interior of such a region are rays which have scattered through an angle between the two generating angles of the cones. Thus any light ray intersecting such a region belongs to the angle class defined by that region. Prior analyzers have employed ring-shaped light detectors to measure the amount of light that scatters in an angle class determined by the radius and width of the ring and its distance from the scattering region. To correlate correctly the detected light with a scattering angle, these ring-shaped detectors must be mounted and aligned precisely perpendicular to the incident beam.
Since the interaction region of the incident beam with the particles generally has a finite extent, multiple particles at different locations in the incident beam will each contribute multiple overlapping cones of scattered light, with the apexes of the cones offset by the distance between the particles. Particles of the same size will have overlapping scattered-light cones of similar intensity variations, whereas particles of different sizes will have overlapping scattered-light cones of different intensity variations.
When the light beam illuminates a sample volume of finite extent, a converging lens may be used to direct parallel rays of light, each by definition scattered through the same scattering angle (by different particles), to a single point on a light detector in the focal plane of the lens. A lens that functions in this manner performs a Fourier transform, so that all light arriving at a given point on the detector is known to have been scattered by the sample through a particular scattering angle, regardless of the location of the scattering particle in the sample volume.
The effect of the converging lens is to transform the spatial distribution of the scattered light it receives to that of an equivalent virtual system in which the light distribution in the focal plane of the lens is the same as if all the scattering particles were located at a point coincident with the optic center of the lens. The light detectors are placed in the focal plane of the lens. The line from the optic center of the lens to the focal point of the lens is usually called the optic axis.
If a scattered ray passes through different refracting media, such as air and a sample suspension fluid, before detection, then an appropriate correction must be applied to the ray's apparent angle of scatter to determine its true angle of scatter. Use of a lens and recognition of the virtual scattering system simplifies the correction.
The intensity of light scattered as a function of scattering angle, when experimentally determined as above for a sample composed of many particles of a range of different sizes, consists of the summation of the scattered light from all the particles. If we assume that each size particle in the sample scatters light according to a given mathematical theory and in proportion the relative number of such size particles present, then it is mathematically possible to determine from the experimental data the relative numbers of each size particle constituting the sample, i.e., to determine the size distribution of the sample. The well-known mathematical process by which the size distribution may extracted from the composite data is called are inversion process, or sometimes a deconvolution process.
In the usual convention, a scattering angle of zero degrees coincides with unscattered light, and a scattering angle of 180 degrees represents light reflecting directly back into the incident beam. Scattering angles between 90 and 180 degrees are termed backscattering.
Light scattering particle size analyzers are typically employed for particles ranging in size from less than one micrometer to several hundred micrometers. Within this size range, and for light in the visible or near-visible portion of the spectrum, the smaller particles tend to scatter light somewhat uniformly in all directions, whereas the larger particles scatter light mostly in the forward direction (small angle with respect to the incident beam direction). However, the larger particles also scatter much more light than the smaller particles. Thus particles of all sizes will contribute to the amount of light scattered in a particular direction. To extract particle size information accurately from measurements of scattered light intensity, a particle size analyzer usually measures the intensity of light scattered at a number of angles relative to the incident beam.
It is important, especially in the forward direction, that a particle size analyzer provide high angular resolution of the light intensity data. It is characteristic of the mathematical inversion process that the number of distinct particle sizes postulated to exist in the sample cannot exceed the number of angular positions for which scattering intensity data values are measured. Therefore, high angular resolution, allowing independent scattering intensity data to be obtained at many closely spaced angles, will enable an analyzer to distinguish the quantity of particles at more closely spaced particle sizes and will lead to more precision and higher resolution in the particle size distribution obtained by the inversion process. A good discussion of the desirability of obtaining high resolution in particle scattering data is contained in the Coulter Corporation Technical Monograph. "LS Series Resolution," which monograph is incorporated by reference.
The problem of achieving an accurate characterization of a given particle distribution may be illustrated with a specific example. Assume that scattering intensity data are obtained for n scattering classes q.sub.i and are represented by the scattering intensity function I(q.sub.i). with i=1, . . . , n. A particular mathematical model, such as (but not limited to) the Mie theory, is chosen to represent the light scattering by the particles in each class. Computations with the theory predict s.sub.ij as the amount of scattering in angle class i for a particle of size j, with j=1, . . . , m. The particle size parameter j represents m particle sizes ranging from 0.1 micrometers to 1000 micrometers. Typically j will represent equally-spaced intervals on a log-based size scale. The particle size distribution S.sub.j is related to the intensity I(.sub.qi) through the matrix equation EQU [I(q.sub.ij ]=[s.sub.ij ][S.sub.j ].
Thus, S.sub.j may be determined through inversion EQU [S.sub.j ]=[s.sub.ij ].sup.-1 [s.sub.ij ][S.sub.j ]=[s.sub.ij ].sup.-1 [I(q.sub.i ]
Since the fortieth root of ten is 1.05925, 40 equally-spaced log intervals per size decade must be employed in the computation of [s.sub.ij ] to achieve a resolution of 6% in the particle size distribution. To achieve this size resolution through four decades (particle sizes ranging from 0.1 micrometers to 1000 micrometers), [s.sub.ij ] must have 160 elements in the j dimension. This implies that the analyzer must employ at least 160 angle classes, and preferably at least 320 classes, to ensure a well-behaved inversion. For an analyzer that operates in the scattering angle range of 0.degree. to 32.degree., 320 angle classes implies an angular resolution of 0.1.degree. if all of the angle classes are equally spaced.
Many prior art devices have addressed the need of a particle size analyzer to achieve high angular resolution and to respond to a wide range of scattered light intensities. For example, U.S. Pat. Nos. 4,953,978, 5,056,918; and 5,104,221, issued to Bott, disclose a plurality of discrete annular silicon photodetector sectors, of circular shape and increasing radius, disposed in a fixed position relative to the nominal beam axis. These detectors are responsive to the cone of scattered light that intersects the detector in a region defined by the circular shape of the detector. Additional silicon photodetectors can be deployed in a line extending beyond the annular detectors, extending the angular range of the analyzer. The intent in these patents is that each of the discrete photodetectors is selected and mounted to be responsive to light scattered in a fixed angular interval with respect to the nominal beam axis. In this manner, the geometrical shape of the photodetector and its intensity response can be configured so that the sensitivity and dynamic characteristics of the detector match the light intensity expected for the angular position of the photodetector. Similar design considerations have been employed by prior art analyzers that employ fixed deployments of ring-shaped photodetectors.
However, the use of fixed deployments of discrete solid-state photodetectors leads to many problems. For example, these deployments require precise calibration and alignment with the light source in order to obtain valid light scattering data. The calibration and alignment must be re-done at any time that a component of the analyzer is moved or changed. Another problem encountered with the use of fixed deployments of discrete photodetectors is that the number and complexity of detectors used increases the cost of the analyzer and increases the chance for malfunction. Solid-state photodetectors provide a current signal which is proportional to the light intensity falling on the photodetector. Thus, great care must be used in measuring the low current resulting from low intensity light.
The most significant problem with prior art analyzers using fixed deployments of discrete photodetectors is the limited number of detector elements used. These analyzers typically employ 16 to 32 detector elements, although some may use as many as 126 elements. In any case, the number used directly limits the resolution (number of unknown independent variables) obtainable in the size distribution. An approximation used by prior devices to overcome this limitation is to assume that a particular functional form, such as a Gaussian distribution, can be used to describe the particle size distribution of a sample. In this way, the number of unknown independent variables is reduced to the two parameters necessary to define the Gaussian curve. Unfortunately, most samples are poorly described by a Gaussian curve, and the validity of such a result is problematic at best. Sometimes size resolution is enhanced by limiting the analyzer to a narrow range of particle sizes, but this technique limits the general utility of the analyzer to determine particle size distributions across a broad variety of sizes.
Other prior art devices use photomultipliers as the light detector, such as described in U.S. Pat. Nos. 4,676,641 and 4,781,460, issued to Bott. Multiple photomultipliers can be used at different angles to the incident beam, or a single photomultiplier can be used and moved through an angle relative to the incident beam to collect data at different scattering angles. The physical size of a photomultiplier (in general, larger that a discrete silicon photodetector) causes problems since a high angular resolution cannot be achieved without masking off a portion of the light entrance window. The masking limits the light entering the photomultiplier and thereby lengthens the exposure time required to obtain sufficient data. In addition, the size of a photomultiplier prohibits the side-by-side mounting of multiple photomultipliers to cover adjacent angle classes. It is therefore necessary to move the photomultiplier to many angular positions to get data, further lengthening the data acquisition time and adding to the complexity of the analyzer. During long data acquisition runs, the particle size characteristics of the sample may change, creating problems for accurate data analysis. Like silicon photodetectors, photomultipliers provide a current signal which is proportional to the light intensity falling on the photomultiplier. Thus, where the intensity is low, the current is low and care must be exercised in reading the current.
A problem common to all of the prior art particle size analyzers is that they must be mechanically or manually aligned. Frequently, the alignment procedure must be performed between data acquisition runs for different samples. Thus prior art analyzers require operator monitoring and intervention on a regular basis, making unattended or automatic operation problematic.
Another problem common to all of prior art analyzers is that their angular resolution is controlled by varying the detector size, by masking of the detector, or by changing other mechanical or opto-mechanical aspects of the devices, generally in the design stage. These techniques of controlling angular resolution imply that the analyzer is not easily re-configured to change the resolution which may be desired for particular experimental needs. Prior art analyzers tend to be configured by the manufacturer for an assumed amount of angular resolution at the various scattering angles provided by the analyzer and no variation is possible.
Prior art analyzers have had particular problems when analyzing particle samples that consist of two or more groups of distinct but nearly identical sizes. This situation causes difficulties in the inversion process unless a very high angular resolution of the scattering data is available. Where sufficiently high resolution is not available, the inversion analysis must be constrained to look for assumed functional fits (i.e., Gaussian, bi-modal or multi-modal Gaussian, etc.) to the experimental data with theoretical size values close to the size values to be determined. The lack of sufficient angular resolution in prior art analyzers has led to the necessity of operator input, in the form of an educated guess as to the make-up of the particle mix or selection of functional constraints, to resolve the two or more groups of particles in the particle size distribution.
Thus, a need exists for a particle size analyzer capable of resolving several hundred angle classes which can be used in varying analytical conditions without physical realignment of the analyzer or guidance from the operator as to the nature of the particle mix under investigation, and which, when compared to the prior art, produces both scattering intensity data over a larger angular range with greatly increased angular resolution and particle size distributions over a larger range of particle sizes with greatly increased size resolution.